Mapping FS space

Attaching package: ‘dplyr’

The following objects are masked from ‘package:stats’:

    filter, lag

The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

Loading in data version 1.127.0

The rescaled vectors (on the right) are what go into Legendre approximation. In this case, these plots should look identical, because all the draws from the feasible set have the same number of individuals as the Portal vector. I have at other times compared SADs without the total abundance constraint, where the rescaled plots could look quite different.

Loading required package: polynom

The green line marks the centroid, and the red line marks the Portal estimation values.

Here we are reconstructing the scaled SAD from the approximated coefficients. The hollow points are estimates from approximation with 8 polynomials, and the stars mark the true values. Using 8 polynomials for a 10-species vector gives us extremely low SSQE. There is no real value for the centroid, but closest_fs is the element of the feasible set with the lowest euclidean distance between its coefficients and the centroid coefficients.

There seems to be some relationship to skewness - skewness locates you in a particular part of the state space. Not sure what that means.

Skewness is not equivalent to centroid distance.